White lines appearing when rendering shadows to separate layer and recombining in compositor
I did a test scene like the one you did.  I thought it was due to the premult setting (usually that's the guilty party for compositing edges), but that's not the case here. 
 Part of it is due to anti-aliasing and the pixel filter - not because of bad settings, but just the nature of it.

With the cube by itself, the edges of the alpha are going white to black, with some grey in the middle.  For the shadow catcher and holdout cube, the edges between the shadow's alpha are going white to grey to black, in the opposite direction.  This edge is on the same pixels for both layers, of course. When you do an alpha over, that edge results in some grey alpha values from both layers competing for the same pixels.  Therefore, some of your white background peeks through and shows up as white

The best solution is, simply, don't composite this.  If you can avoid compositing layers of the same CG scene, render the shadow and object together.  My guess is you want to do this for visual effects; I do that too and run into this situation often.  I usually render the shadow together with any CG object I'm putting in a video to get a clean edge.

If you must composite them together, you can do some masking and simply expand the shadow layer's alpha edge with a dilate/erode node.  That can get messy and give strange results, but it's possible.